Detecting and reconstructing subdivision connectivity |
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Authors: | Gabriel Taubin |
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Affiliation: | (1) California Institute of Technology, Department of Electrical Engineering, MS-136-93, Pasadena, CA 91125, USA E-mail: taubin@caltech.edu, US |
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Abstract: | inverse subdivision algorithms , with linear time and space complexity, to detect and reconstruct uniform Loop, Catmull–Clark, and Doo–Sabin subdivision
structure in irregular triangular, quadrilateral, and polygonal meshes. We consider two main applications for these algorithms.
The first one is to enable interactive modeling systems that support uniform subdivision surfaces to use popular interchange
file formats which do not preserve the subdivision structure, such as VRML, without loss of information. The second application
is to improve the compression efficiency of existing lossless connectivity compression schemes, by optimally compressing meshes
with Loop subdivision connectivity. Our Loop inverse subdivision algorithm is based on global connectivity properties of the
covering mesh, a concept motivated by the covering surface from Algebraic Topology. Although the same approach can be used for other subdivision schemes, such as Catmull–Clark, we
present a Catmull–Clark inverse subdivision algorithm based on a much simpler graph-coloring algorithm and a Doo–Sabin inverse
subdivision algorithm based on properties of the dual mesh. Straightforward extensions of these approaches to other popular
uniform subdivision schemes are also discussed.
Published online: 3 July 2002 |
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Keywords: | : Inverse subdivision – 3D file formats – Geometry compression – Algorithms – Graphics |
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